Elliptic curve search results

Results (6 matches)

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Label	Class	Class size	Class degree	Base field	Field degree	Field signature	Conductor	Conductor norm	Discriminant norm	Root analytic conductor	Bad primes	Rank	Torsion	CM	CM	Sato-Tate	$\Q$-curve	Base change	Semistable	Potentially good	Nonmax $\ell$	mod-$\ell$ images	$Ш_{\textrm{an}}$	Tamagawa	Regulator	Period	Leading coeff	j-invariant	Weierstrass coefficients	Weierstrass equation
63.1-a3	63.1-a	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	63.1	$3^{2} \cdot 7$	$3^{4} \cdot 7^{2}$	$1.33215$	$(-a+2), (-a-2), (a)$	0	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$1$	$13.02432697$	1.230683220	$\frac{103823}{63}$	$\bigl[1$ , $0$ , $0$ , $1$ , $0\bigr]$	${y}^2+{x}{y}={x}^{3}+{x}$
63.1-b3	63.1-b	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	63.1	$3^{2} \cdot 7$	$3^{4} \cdot 7^{2}$	$1.33215$	$(-a+2), (-a-2), (a)$	$1$	$\Z/4\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓	✓		$2$	2B	$1$	$2^{3}$	$0.373149604$	$14.60752776$	1.030103091	$\frac{103823}{63}$	$\bigl[a$ , $1$ , $a$ , $0$ , $0\bigr]$	${y}^2+a{x}{y}+a{y}={x}^{3}+{x}^{2}$
441.1-a3	441.1-a	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	441.1	$3^{2} \cdot 7^{2}$	$3^{4} \cdot 7^{8}$	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$1$	$5.213351238$	1.970461553	$\frac{103823}{63}$	$\bigl[a$ , $-a - 1$ , $1$ , $-330 a + 873$ , $-1537 a + 4066\bigr]$	${y}^2+a{x}{y}+{y}={x}^{3}+\left(-a-1\right){x}^{2}+\left(-330a+873\right){x}-1537a+4066$
441.1-f3	441.1-f	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	441.1	$3^{2} \cdot 7^{2}$	$3^{4} \cdot 7^{8}$	$2.16684$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓				$2$	2B	$1$	$2^{3}$	$1$	$5.213351238$	1.970461553	$\frac{103823}{63}$	$\bigl[1$ , $a - 1$ , $a$ , $-330 a + 873$ , $1537 a - 4068\bigr]$	${y}^2+{x}{y}+a{y}={x}^{3}+\left(a-1\right){x}^{2}+\left(-330a+873\right){x}+1537a-4068$
567.1-c3	567.1-c	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	$1$	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1.319254411$	$4.341442324$	4.329558047	$\frac{103823}{63}$	$\bigl[a$ , $-1$ , $0$ , $9$ , $0\bigr]$	${y}^2+a{x}{y}={x}^{3}-{x}^{2}+9{x}$
567.1-l3	567.1-l	$8$	$16$	$\Q(\sqrt{7})$	$2$	$[2, 0]$	567.1	$3^{4} \cdot 7$	$3^{16} \cdot 7^{2}$	$2.30735$	$(-a+2), (-a-2), (a)$	0	$\Z/2\Z$	$\textsf{no}$		$\mathrm{SU}(2)$	✓	✓			$2$	2B	$1$	$2^{3}$	$1$	$4.869175922$	1.840375511	$\frac{103823}{63}$	$\bigl[1$ , $-1$ , $0$ , $9$ , $0\bigr]$	${y}^2+{x}{y}={x}^{3}-{x}^{2}+9{x}$

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  *The rank, regulator and analytic order of Ш are not known for all curves in the database; curves for which these are unknown will not appear in searches specifying one of these quantities.